27-1/ 若a>0,b>0,a*b>1,log(1/2)[a]=ln2,则log(a)[b]与log(1/2)[a]的关系是：（）?

题目

27-1/ 若a>0,b>0,a*b>1,log(1/2)[a]=ln2,则log(a)[b]与log(1/2)[a]的关系是：（）?
(A)log(a)b< log(1/2)[a]
(B)log(a)b= log(1/2)[a]
(C)log(a)b>log(1/2)[a]
(D)log(a)b与log(1/2)[a] 无法比较大小
我做到一半就做不下去了：
a=(1/2)^(ln2)
log(1/2)[a]=log(1/2) [(1/2)^(ln2)]=ln2
请写出详细过程及思路.

答案

a=(1/2)^(ln2)
a*b>1
b/(2^ln2)>1
因为ln2>0
2^ln2>1>0
b>2^ln2>1
alog(a)b